i n s u p p o r t i n g e n v i r o n m e n t a l s u s t a i n a b i l i t y, m a n a g i n g p r o d u c t r e t u r n s h a s b e c o m e a v e r y i m p o r t a n t a n d c h a l l e n g i n g i s s u e. r e s p o n d i n g t o t h i s t r e n d, r e s e a r c h e r s i n m a n y p a r t s o f t h e w o r l d h a v e c o n d u c t e d n u m e r o u s s t u d i e s i n r e v e r s e l o g i ...

gp(X) = {x1 x2 2 . . . x n n | xi ∈ X, i = ±1} Définition 1.1. Soit X un ensemble. Un produit (ou suite) w = x1 x2 2 . . . x n n , | xi ∈ X, i = ±1 s’appelle un X–mot (ou mot) de longueur n. Si on considère les xi comme des éléments du groupe G, ce mot a une valeur g dans G, et nous écrivons x1 x2 2 . . . x n n =G g (certains écrivent w). Définition 1.2. On dit que le X–mot w = x1 x2 2 . . . x ...

From (15) and (II), it follows that because N(0) = IV(O). The resulting estimate of X(w) is given by m bee (2211 c J(Wi-w/&(w) = J(w-Wk), k = 1,. .. ,m. (16) i=l With Aik the elements of the inverse of a matrix whose elements X(w) = X(w) + &) [N(w)-iv(O) +$q equal d(wi-wk), the system (16) yields and the mean-square error by [see (21)] m @i(w) = C A;J(w-wk). k=l (17) From (16), it follows that ...

To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...

We study Liouville type of theorems for the Navier-Stokes and the Euler equations on R N , N ≥ 2. Specifically, we prove that if a weak solution (v, p) satisfies |v| 2 +|p| ∈ L 1 (0, T ; L 1 (R N , w 1 (x)dx)) and R N p(x, t)w 2 (x)dx ≥ 0 for some weight functions w 1 (x) and w 2 (x), then the solution is trivial, namely v = 0 almost everywhere on R N × (0, T). Similar results hold for the MHD ...

We announce some asymptotics for orthogonal and extremal polynomials associated with exponential weights W = exp ( Q). 1 Classes of Weights Let I be a nite or in nite interval and let Q : I ! [0;1) be convex. Let W := exp ( Q) and assume that all power moments Z I xW (x)dx; n = 0; 1; 2; 3; ::: are nite. Then we may de ne orthonormal polynomials pn(x) = pn(W ; x) = n(W )x + : : : ; n(W ) > 0;

Let d(n; q) be the number of labeled graphs with n vertices, q N = ? n 2 edges, and no isolated vertices. Let x = q=n and k = 2q ?n. We determine functions w k 1, a(x), and '(x) such that d(n; q) w k ? N q e n'(x)+a(x) uniformly for all n and q > n=2.

abstract the aim of this study is laboratory investigation of nitrate reduction in water using fe/cu nano particles. in this regards, nano fe0 (54±4 nm) and fe/cu particles (75±3 nm) was synthesized and characterized by x-ray diffraction pattern (xrd), scanning electron microscope (sem) and transmission electron microscopy (tem) photographs. the effects of coating load of nano-fe0 by cu (0, 5, ...